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  1. Origin

    Linked via "Cartesian space"

    Origin in Geometry and Calculus
    In coordinate systems, the Origin serves as the zero-point reference, denoted classically as $\mathbf{O}$. In two-dimensional Cartesian space{: .cartesian-space}, it is the intersection of the axes, $(0, 0)$, and in three dimensions, it is $(0, 0, 0)$.
    Mathematical Significance

  2. Pythagorean Theorem

    Linked via "Cartesian space"

    Three Dimensions
    In three-dimensional Cartesian space, given a rectangular prism with dimensions $x, y, z$, the length of the space diagonal $d$ is found by applying the theorem sequentially:
    $$d^2 = x^2 + y^2 + z^2$$

  3. Spatial Coordinate

    Linked via "Cartesian space"

    $r$: The radial distance from the $Z$-axis (the rotational axis).
    $\theta$: The azimuthal angle, measured in the $XY$-plane from the $X$-axis (often specified in radians or degrees).
    $z$: The perpendicular distance from the $XY$-plane, analogous to the $z$-coordinate in Cartesian space.
    Conversion from Cartesian $(x, y, z)$ to Cylindrical $(r, \theta, z)$ is defined by: